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This page features an animated roller coaster with two loops. Energy bar graphs show the transformation of energy from potential to kinetic as the roller coaster descends the initial hill. As the car continues on the track, users can visualize how kinetic energy is dependent upon an object's mass and its speed. This animation is an example of a system in which TME (Total Mechanical Energy) remains the same during the course of the motion. It is part of The Physics Classroom, a collection of online tutorials for high school physics students.

Standards (14)

AAAS Benchmark Alignments (2008 Version)

4. The Physical Setting

4E. Energy Transformations

9-12: 4E/H1. Although the various forms of energy appear very different, each can be measured in a way that makes it possible to keep track of how much of one form is converted into another. Whenever the amount of energy in one place diminishes, the amount in other places or forms increases by the same amount.

9-12: 4E/H9. Many forms of energy can be considered to be either kinetic energy, which is the energy of motion, or potential energy, which depends on the separation between mutually attracting or repelling objects.

4F. Motion

9-12: 4F/H1. The change in motion (direction or speed) of an object is proportional to the applied force and inversely proportional to the mass.

Next Generation Science Standards

Energy (HS-PS3)

Students who demonstrate understanding can: (9-12)

Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known. (HS-PS3-1)

Disciplinary Core Ideas (K-12)

Definitions of Energy (PS3.A)

Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system's total energy is conserved, even as, within the system, energy is continually transferred from one object to another and between its various possible forms. (9-12)

At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy. (9-12)

Conservation of Energy and Energy Transfer (PS3.B)

When the motion energy of an object changes, there is inevitably some other change in energy at the same time. (6-8)

Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems. (9-12)

Mathematical expressions, which quantify how the stored energy in a system depends on its configuration (e.g. relative positions of charged particles, compression of a spring) and how kinetic energy depends on mass and speed, allow the concept of conservation of energy to be used to predict and describe system behavior. (9-12)

Common Core State Standards for Mathematics Alignments

High School — Algebra (9-12)

Creating Equations? (9-12)

A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

High School — Functions (9-12)

Interpreting Functions (9-12)

F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.?

F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Common Core State Reading Standards for Literacy in Science and Technical Subjects 6—12

Integration of Knowledge and Ideas (6-12)

RST.11-12.9 Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible.

Range of Reading and Level of Text Complexity (6-12)

RST.9-10.10 By the end of grade 10, read and comprehend science/technical texts in the grades 9—10 text complexity band independently and proficiently.

Units (3)

This resource is part of 3 Physics Front Topical Units.

Topic: Kinematics: The Physics of MotionUnit Title: The Case of Roller Coasters

Short tutorial that uses an animation to illustrate the work/energy relationship in a roller coaster. The author breaks down the associated equation to show how total mechanical energy is conserved in the system.

For teachers wanting some background information on energy transformation: this tutorial features an animated roller coaster with moving bar graphs that depict kinetic and potential energy as the car descends and climbs. It is a great example of a system in which TME (Total Mechanical Energy) remains the same during the course of the motion.

This tutorial features an animated roller coaster with moving bar graphs that depict kinetic and potential energy as the car descends and climbs. It is an example of a system in which TME (Total Mechanical Energy) remains the same during the course of the motion.

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The Physics Classroom: Energy Transformation on a Roller Coaster:

This item is an animation of a skier descending a slope and encountering the force of friction at the end of the run. It contains four energy bar graphs depicting KE, PE, Work, and TME (Total Mechanical Energy). It differs from the Roller Coaster animation in that it illustrates a system where TME is lost due to friction.